"provable that" is correct and usable in written English
You can use it when you want to express that something is able to be shown to be true. For example, "It is provable that the universe is expanding."
"Perhaps things are now provable that weren't provable years ago".
If in the process, new things are provable that were not provable before, so much the better, provided the proprieties are respected.
This leaves Gödel's results completely intact as they concerned what is provable, that is, derivable from the null set of premises or from any one consistent axiomatization of mathematical truths.
"There are facts that are empirical, that are provable, that are confirmable".
"It's provable that it will have that impact," Professor Safranek said.
Also, it is provable that the throughput is optimal for LWDF [35].
"Fundamentally, almost no one coming from the Dominican Republic to the United States is coming here because they have a provable skill that would benefit us and that would indicate their likely success in our society," Sessions said at the time.
Conversations with Russians can spiral into an epistemological abyss, where nothing is provable except that everything is not what it seems.
Except in "limited, narrow circumstances," he said, federal prosecutors must seek to bring charges for "the most serious, readily provable offense" that can be supported by the facts of the case.
This formalization project made sense only if the syntax of mathematics was consistent, for otherwise every syntactical statement would be provable, including that which asserts the consistency of mathematics.
For George Will, a respected right-wing polemicist, to agree in this uniquely provable context that FDR indeed hurt the economy by cutting government spending and trying to balance the budget is to abandon everything the right-wing preaches.
